Question

Express the function 1 Ef o < X LT flx) = sin 2x if TL x <211 if x720 -y e step functions in terms of the unit

Answer 1

$f(x)= \left\{\begin{matrix} 1,\:\:\:\:\:\:\: 0\leq x<\pi \\ \sin(2x), \:\:\:\:\:\pi \leq x<2 \pi \\ e^{-x}, \:\:\:\:\:\: x\geq 2 \pi \end{matrix}\right.$

.

$f(x)=1\left(u\left(t-0\right)-u\left(t-\pi \right)\right)+\sin \left(2x\right)\left(u\left(t-\pi \right)-u\left(t-2\pi \right)\right)+e^{-x}\left(u\left(t-2\pi \right)-u\left(t-\infty \right)\right)$

$f(x)= 1\left(1-u\left(t-\pi \right)\right)+\sin \left(2x\right)\left(u\left(t-\pi \right)-u\left(t-2\pi \right)\right)+e^{-x}\left(u\left(t-2\pi \right)-0\right)$

$f(x)= 1-u\left(t-\pi \right)+\sin \left(2x\right)\left(u\left(t-\pi \right)-u\left(t-2\pi \right)\right)+e^{-x}u\left(t-2\pi \right)$